Based on the basic physical meaning of error and error variety , this paper analyzes the logical relationship between them and uses Universal Combinatorial Operation Model in Universal Logic to describe it. Accordingly, a flexible logic control method is put forward to realize effective control on multivariable nonlinear system. In order to implement fusion control with artificial neural network, this paper proposes a new neuron model of Zero-level Universal Combinatorial Operation in Universal Logic. And the artificial neural network of flexible logic control model is implemented based on the proposed neuron model. Finally, stability control, anti-interference control of double inverted-pendulum system, and free walking of cart pendulum system on a level track are realized, showing experimentally the feasibility and validity of this method. 1. Introduction In recent years, fuzzy control has made a rapid development, and it has found a considerable number of successful industrial applications [1–3]. But fuzzy control has two shortcomings in the process of controlling some practical complex systems. One is that the number of control rules increases exponentially with the increase of the number of inputs, and the other one is that the precision of control system is low [4]. To reduce the dimension of control model, hierarchical fuzzy logic control divides the collection of control rules into several collections based on different functions [5, 6]. Compound control combines fuzzy control and other relatively mature control methods to realize the effective control [7], such as Fuzzy-PID Compound Control [8], fuzzy predication control [9], adaptive fuzzy control [10], and so forth. The basic idea of adaptive fuzzy control based on variable universe [11, 12] is to keep the form of rules and varies universe of discourse according to the control error. Though a great deal of research has been done to improve the performance of fuzzy control, most of these methods are based on the basic idea that fuzzy controller is a piecewise approximator. However, to date, there has been relatively little research conducted on the internal relations among input variables of fuzzy controllers. Based on analysis of the logical relationship between the system’s error and error variety , this paper indicates that the relationship is just universal combinatorial relation in Universal Logic [13], and the simple Universal Combinatorial Operation can be used instead of complex fuzzy rule-based reasoning process. As a result, a flexible logic control method is proposed to realize
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